$\int a^{a^{a^x}} . a^{a^{a^x}} . a^x dx$ is equal to
Answer & explanation
Correct answer: option 3
Put ax = t
∴ I = $\int \frac{a^{a^t} . a^t d t}{\log a}$
again put at = z
∴ I = $\int \frac{a^z d z}{\log a}=\frac{a^z}{(\log a)^3}+c=\frac{a^{a^{a^x}}}{(\log a)^3}+c$
Hence (3) is the correct answer.